Crawley had come from behind after Danny Holmes put Rovers ahead through Josh Simpson and Kyle McFadzean.
But Jake Cassidy equalised, and scored a second after Jean-Louis Akpa Akpro had made it 2-3.
Andy Robinson sealed the win with Tranmere’s fifth on the break giving Ronnie Moore’s side 20 points from eight fixtures.
Meanwhile at Meadow Lane, Yoann Arquin netted once in each half either side of Alan Judge’s long-range strike as Keith Curle’s County wrapped up three points by the hour mark against Portsmouth.
Stevenage fell out of the top two after another draw, this time 1-1 away to Doncaster.
The latest point buts undefeated Stevenage one behind Notts County in third and two ahead of the three sides also occupying the play-off zone – MK Dons, who won 4-1 away at bottom club Bury; Swindon, who thrashed Bournemouth at home 4-0; and Sheffield United, who won at Yeovil 1-0 via Neill Collins’ only goal.
Walsall are also on 14 points after seeing off Preston North End 3-1 at home, while Brentford also held fort with a 1-0 victory over Oldham and Leon Clarke was again the hero for Scunthorpe with the decisive goal in their win by the same scoreline over visiting Colchester.
Coventry, relegated from the Championship, find themselves in the bottom four after a 1-2 reverse at home to Carlisle in Mark Robins’ first game in charge.
Leyton Orient came from behind to claim a 1-1 draw at Crewe, while Hartlepool left it late to avoid defeat at home to Shrewbury after Andy Monkhouse levelled in stoppage time.